I've got a 1992 Caddy Deville that we bought used a few weeks ago. Last night the engine stalled due to insufficient electrical power, so this morning I replaced the alternator and the battery. Tonight driving home it ran out of electrical power again. Does anyone have an idea what'* going on?

For the most part, the charging system is the alternator, the battery, and the cables. Seeing that you already changed two parts. I would be looking at the cables, start with checking the connections. Also pull back the boots and look where the connection is crimped to the wire. If it'* green or corroded, replace the cables.